Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x + 2$ and $ BC = 5x + 34$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x + 2} = {5x + 34}$ Solve for $x$ $ 4x = 32$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({8}) + 2$ $ BC = 5({8}) + 34$ $ AB = 72 + 2$ $ BC = 40 + 34$ $ AB = 74$ $ BC = 74$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {74} + {74}$ $ AC = 148$